A MEMS resonator provided with a beam-shaped vibration portion where both edges are fixed, and an electrode provided near this vibration portion is known (for example, refer to patent document 1 and non-patent document 1). The resonator described in patent documents 1 and non-patent document 1 (it is also hereafter referred to “conventional type resonator”) vibrates the vibration portion using the change of electrostatic capacity of the vibration portion which occurs by impressing alternating voltage to the electrode.
It is known that resonance frequency “f0” of the vibration portion is given by the following (1) formulas:f0=(½π){(km−ke)/mr}0.5   (1)where “km” is a spring constant of the vibration portion, “ke” is a spring constant of the vibration portion in the state where bias voltage is impressed, and “mr” is the effective mass of the vibration portion.
As cleared by equation (1), resonance frequency f0 depends on “km”, “ke”, and “mr”. Incidentally, “km”, “ke”, and “mr” are greatly influenced by the size (length, width, and thickness) of the vibration portion.
Therefore, when fabricating two or more resonators equal to resonance frequency “f0”, it is necessary to form a vibration portion with sufficient accuracy of dimension.
[Patent Document 1] Japanese Patent Publication JP2006-5731A
[Non-patent document 1] Frank D. Bannon, III, et al, “High-QHF Microelectromechanical Filters”, IEEE Journal of solid-state circuits, Vol. 35, No. 4, April, 2000, pp 512-526
However, in fabricating of the above-mentioned conventional type resonator, there was a problem that a dimension error is easy to be introduced into the vibration portion by a formation process of the vibration portion. Hereafter, this problem will be explained in detail.
Generally, the vibration portion is formed of dry etching. Incidentally, when patterning by dry etching, it is known that the so-called “micro loading effect” from which an etching rate changes according to roughness and fineness of a formed photoresist pattern occurs. That is, an etching rate becomes relatively slower in an area with high pattern density, and conversely, an etching rate becomes relatively faster in an area with low pattern density.
This micro loading effect causes an uncontrollable error to occur depending on pattern density near the vibration portion in a size of the vibration portion. As a result, resonance frequency f0 of a resonator will shift from a designed value.